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Unfortunately, the RC records for that area do not start until 1884 except for marriage records from 1810-1812. I did look at the Tithe records from the 1820s with no records for Nolan or Doherty. The 1855 Griffiths Valuation head of household listing for Donanaghta civil parish shows a Patrick Dogherty on River St. in Eyrecourt http://www.failteromhat.com/griffiths/galway/donanaghta.htm
You may want to post the story of James and Julia on our XO Chronicles site https://www.irelandxo.com/ireland-xo/history-and-genealogy/ancestor-data...
You may also want to consider autosomal DNA testing.